Question

The number of mosquitoes in anchorage, alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: m(x)=-x^2+14xm(x)=−x 2 +14xm, left parenthesis, x, right parenthesis, equals, minus, x, start superscript, 2, end superscript, plus, 14, x how many centimeters of rain will produce the maximum number of mosquitoes?

Answer 1

Explanation:

49 million misquitos

Answer 2

m (x) = - x ^ 2 + 14x
To find the maximum function, the first thing to do is to obtain the first derivative:
m '(x) = - 2x + 14
We match zero:
0 = -2x + 14
We clear x:
x = 14/2 = 7
x = 7

We verify that this value is a maximum through the second derivative:
m '' (x) = - 2
m '' (7) = - 2 (<0 therefore it is a maximum)

Answer:
7 centimeters of rain will produce the maximum number of mosquitoes.